Value at Risk and Extreme Value Theory: Application To The Johannesburg Securities Exchange

Abstract

Value at Risk (VaR) has been established as one of the most important and commonly used financial risk management tools. Nevertheless, the attractive features and wide-spread use of VaR could not help to avoid a number of financial crises and its severe impact on economies globally, the latest being the 2008 financial crisis. In isolation, VaR has, in the past, mostly focused on events that occur with a 1% or 5% probability. This is a popular reason offered for its failure of ‘predicting’ the financial crises, as the latter are viewed as ‘extreme’ events and can therefore not be classified as events with a 1% or 5% probability of happening. The use of Extreme Value Theory (EVT) in calculating VaR is a relatively new approach and attempts to expand on the traditional VaR-only approach to include potential extreme events. This approach has provided good results in developed markets and in this article we investigate if the same holds true in the more volatile South African equity space. We examine and compare the application of seven VaR and VaR-EVT models on the FTSE/JSE Total Return All Share Index. Our results suggest that the Filtered Historical Simulation VaR method is the best all-round model. It is, however, worthwhile to employ EVT in the form of the conditional Generalized Pareto Distribution (GPD) model when calculating very extreme quantiles such as the 0.1% quantile. Our results further highlight the importance of filtering the data in order to account for the conditional heteroskedasticity of the financial time series.

Notes

1 The table of summary statistics is available from the authors on request.

2 Tables with results of fitting the GARCH models are available from the authors on request.

3 A detailed discussion on the approach followed to determine the threshold level used in our study is available on request.

4 Results and graphs are available from the authors on request.